snap perpendicular to an edge/line like in CAD
It can be frustrating in other ways, but this just happens to be what the Blender snap system does without add-ons.


Set snap to 'Vertex' and 'Active'
CtrlAltSpace Create a Custom Orientation from side B. (Check 'Use after creation')
K Cut an edge from side A to side B
With Snap on,  G Y Ymove point B up and down its edge


When you hover over point A, it will snap to  the point on side B from which a perpendicular is dropped to it.

What if the new edge isn't in the right place?


Cut another edge, and  G G slide it up and down the face, making the edge parallel to the correctly oriented one by hitting  E, and  F if necessary.